from The Century Dictionary and Cyclopedia

n. (-riz.). A person invested with full power to transact any business; specifically, an ambassador or envoy to a foreign court, furnished with full powers to negotiate a treaty or to transact other business.

Probably the biggest single change was the introduction of the telegraph in the middle of the 19th century, which meant that ambassadors were no longer truly "plenipotentiary", as they are still formally described, since they were within range of instructions and no longer had the necessity or the authority to stand in place of their sovereigns.

In witness whereof we the undersigned, their ministers plenipotentiary, have in their name and in virtue of our full powers, signed with our hands the present definitive treaty and caused the seals of our arms to be affixed thereto.

The euro, in this context, was less a leap into the unknown than an attempt to return to an older discipline, one in which governments would not rely on plenipotentiary central banks to bail them out of their policy errors.